Analysis of transport phenomena and electrochemical reactions in a micro PEM fuel cell with nature inspired flow field design

E NERGY AND E NVIRONMENTVolume 6, Issue 1, 2015 pp.1-16 Journal homepage: www.IJEE.IEEFoundation.org Analysis of transport phenomena and electrochemical reactions in a micro PEM fuel c

E NERGY AND E NVIRONMENT

Volume 6, Issue 1, 2015 pp.1-16

Journal homepage: www.IJEE.IEEFoundation.org

Analysis of transport phenomena and electrochemical reactions in a micro PEM fuel cell with nature

inspired flow field design

Maher A.R Sadiq Al-Baghdadi

Fuel Cell Research Center, International Energy and Environment Foundation, Najaf, P.O.Box 39, Iraq

Abstract

Micro-fuel cells are considered as promising electrochemical power sources in portable electronic devices The presence of microelectromechanical system (MEMS) technology makes it possible to manufacture the miniaturized fuel cell systems The majority of research on micro-scale fuel cells is aimed at micro-power applications Performance of micro-fuel cells are closely related to many factors, such as designs and operating conditions CFD modeling and simulation for heat and mass transport in micro PEM fuel cells are being used extensively in researches and industrial applications to gain better understanding of the fundamental processes and to optimize the micro fuel cell designs before building a prototype for engineering application In this research, full three-dimensional, non-isothermal computational fluid dynamics model of a micro proton exchange membrane (PEM) fuel cell with nature inspired flow field designs has been developed The design inspired from the existed biological fluid flow patterns in the leaf This comprehensive model accounts for the major transport phenomena such as convective and diffusive heat and mass transfer, electrode kinetics, transport and phase-change mechanism of water, and potential fields in a micro PEM fuel cell The model explains many interacting, complex electrochemical, and transport phenomena that cannot be studied experimentally

Copyright © 2015 International Energy and Environment Foundation - All rights reserved

Keywords: PEM fuel cells; Micro fuel cell; Nature inspired flow channels; Electrochemical; Heat

transfer; CFD

1 Introduction

Fuel cell system is an advanced power system for the future that is sustainable, clean and environmental friendly Small fuel cells have provided significant advantages in portable electronic applications over conventional battery systems Competitive costs, instant recharge, and high energy density make fuel cells ideal for supplanting batteries in portable electronic devices Micro fuel cells belong to the category

of portable fuel cells, but are used in the miniaturized electronic devices with low power, such as micro sensors The presence of microelectromechanical system (MEMS) technology makes it possible to manufacture the miniaturized fuel cell systems for application in portable electronic devices The majority of research on micro-scale fuel cells is aimed at micro-power applications There are many new miniaturized applications which can only be realized if a higher energy density power source is available compared to button cells and other small batteries

The development of physically representative models that allow reliable simulation of the processes under realistic conditions is essential to the development and optimization of fuel cells, the introduction

of cheaper materials and fabrication techniques, and the design and development of novel architectures The difficult experimental environment of fuel cell systems has stimulated efforts to develop models that could simulate and predict multi-dimensional coupled transport of reactants, heat and charged species using computational fluid dynamic (CFD) methods These models can generally be characterized by the scope of the model In many cases, modeling efforts focus on a specific part or parts of the fuel cell, like the cathode catalyst layer [1], the cathode electrode (gas diffusion layer plus catalyst layer) [2-4], or the membrane electrode assembly (MEA) [5] These models are very useful in that they may include a large portion of the relevant fuel cell physics while at the same time having relatively short solution times However, these narrowly focused models neglect important parts of the fuel cell making it impossible to get a complete picture of the phenomena governing fuel cell behavior Models that include all parts of a fuel cell are typically two- or three-dimensional and reflect many of the physical processes occurring within the fuel cell [6–16] In a real PEM fuel cell geometry, the gas diffusion layers are used to enhance the reaction area accessible by the reactants The effect of using these diffusion layers is to allow a spatial distribution in the current density on the membrane in both the direction of bulk flow and the direction orthogonal to the flow but parallel to the membrane This two-dimensional distribution cannot

be modeled with the well-used two-dimensional models where the mass-transport limitation is absent in the third direction Berning et al [13] used the unified approach to develop a three-dimensional model of

a straight gas flow channels fuel cell The model studied reactant concentrations, current density distributions and temperature gradients within the cell as well as water flux and species transport

Nguyen et al [14] developed a three-dimensional model, which accounts for mass and heat transfer, current and potential distribution within a cell using a one turn serpentine flow field Their results show that oxygen concentration along the gas channels decrease in the direction of flow Also, in the gas diffusion layer, the oxygen concentration is a minimum under the land area At high current densities the oxygen is almost completely depleted under the land areas The result is an uneven distribution of oxygen concentration along the catalyst layer resulting in local overpotentials, which vary spatially

Um and Wang [15] used a three-dimensional model to study the effects an interdigitated flow field The model accounted for mass transport, electrochemical kinetics, species profiles and current density distribution within the cell Interdigitated flow fields result in forced convection of gases, which aids in liquid water removal at the cathode This would help improve performance at high current densities when transport limitations due to excessive water production are expected The model shows that there is little to no difference at low to medium current densities between an interdigitated flow field and a conventional flow field However, at higher current densities, a fuel cell with an interdigitated flow field has a limiting current, which is nearly 50% greater than an equivalent cell with a conventional flow field Al-baghdadi [16] developed a three-dimensional model to investigate the performance of tubular-shaped PEM fuel cell The results show that higher power densities are achieved with the tubular design mainly because of lower activation and diffusion overpotentials Better gas replenishment at the catalyst sites in tubular design results in lower and quite uniform distribution of activation and diffusion potentials

In this work, a multi-phase, non-isothermal, fully three-dimensional CFD model of a micro PEM fuel cell with nature inspired flow field designs has been developed The design inspired from the existed biological fluid flow patterns in the leaf The model accounts for detailed species mass transport, heat transfer in the solids as well as in the gases, potential losses in the gas diffusion layers and membrane, electrochemical kinetics, and the transport of water through the membrane

2.1 Computational domain

The full computational domains for the micro PEM fuel cell consist of cathode and anode gas flow fields, and the MEA are shown in Figure 1

2.2 Model equations

2.2.1 Gas flow channels

In the fuel cell channels, the gas-flow field is obtained by solving the steady-state Navier-Stokes equations, i.e the continuity equation, the mass conservation equation for each phase yields the volume fraction ( )r and along with the momentum equations the pressure distribution inside the channels The continuity equation for the gas phase inside the channel is given by;

(a)

(b) Figure 1 (a) Fluid distribution patterns in nature (leaf), and (b) three-dimensional computational domain

of the micro PEM fuel cell with nature inspired gas flow channels

( ) = 0

⋅

∇ rgρgug (1) and for the liquid phase inside the channel becomes;

⋅

∇ rlρlul (2)

where u is velocity vector [m/s], ρ is density [kg/m3]

Two sets of momentum equations are solved in the channels, and they share the same pressure field Under these conditions, it can be shown that the momentum equations becomes;

( ) [ ( )T]

g g g

g g

g g g g

⎠

⎞

⎜

⎝

−∇

=

∇

−

⊗

⋅

3

2

(3)

l l l

l l

l l l

l

⎠

⎞

⎜

⎝

−∇

=

∇

−

⊗

⋅

3

2

(4)

where P is pressure (Pa), µ is viscosity [kg/(m⋅s)]

The mass balance is described by the divergence of the mass flux through diffusion and convection

Multiple species are considered in the gas phase only, and the species conservation equation in

multi-component, multi-phase flow can be written in the following expression for species i;

0

⎥

⎥

⎥

⎥

⎦

⎤

⎢

⎢

⎢

⎢

⎣

⎡

∇ +

⋅

+

⎥

⎦

⎤

⎢

⎣

⎟

⎠

⎞

⎜

⎝

−

⋅

=

T

T D y

r

P

P y x M

M y y M

M D y

r

T i g i

g

g

N

j

j j j

j j ij i

g

g

u

ρ

ρ

(5)

where T is temperature (K), y is mass fraction, x is mole fraction, D is diffusion coefficient [m2/s]

Subscript i denotes oxygen at the cathode side and hydrogen at the anode side, and j is water vapour in

both cases Nitrogen is the third species at the cathode side

The Maxwell-Stefan diffusion coefficients of any two species are dependent on temperature and

pressure They can be calculated according to the empirical relation based on kinetic gas theory [17];

2 2

3 3

3 75

⎥

⎥

⎦

⎤

⎢

⎢

⎣

⎡ +

⎥

⎥

⎦

⎤

⎢

⎢

⎣

⎡

⎟

⎠

⎞

⎜

⎝

⎛ +

⎟

⎠

⎞

⎜

⎝

⎛

×

=

∑

∑

−

j i

k kj k

ki

ij

M M V

V

P

T

In this equation, the pressure is in atm and the binary diffusion coefficient Dij is in [cm2/s]

The values for ( ∑V ki) are given by Fuller et al [17]

The temperature field is obtained by solving the convective energy equation;

⋅

where Cp is specific heat capacity [J/(kg.K)], k is gas thermal conductivity [W/(m.K)]

The gas phase and the liquid phase are assumed to be in thermodynamic equilibrium; hence, the

temperature of the liquid water is the same as the gas phase temperature

2.2.2 Gas diffusion layers

The physics of multiple phases through a porous medium is further complicated here with phase change

and the sources and sinks associated with the electrochemical reaction The equations used to describe

transport in the gas diffusion layers are given below Mass transfer in the form of evaporation

( m phase > 0 ) and condensation ( m phase < 0 ) is assumed, so that the mass balance equations for both

phases are;

( − sat g g) = m phase

⋅

( sat l l) = m phase

⋅

where sat is saturation, ε is porosity

The momentum equation for the gas phase reduces to Darcy’s law, which is, however, based on the

relative permeability for the gas phase( )KP The relative permeability accounts for the reduction in pore

space available for one phase due to the existence of the second phase [18]

The momentum equation for the gas phase inside the gas diffusion layer becomes;

g = − 1 − sat Kp ∇ P µ

where KP is hydraulic permeability [m2]

Two liquid water transport mechanisms are considered; shear, which drags the liquid phase along with

the gas phase in the direction of the pressure gradient, and capillary forces, which drive liquid water from

high to low saturation regions [18] Therefore, the momentum equation for the liquid phase inside the gas diffusion layer becomes;

sat sat

P KP P

l l

l

l

∂

∂ +

∇

−

=

µ µ

where Pc is capillary pressure [Pa]

The functional variation of capillary pressure with saturation is prescribed following Leverett [18] who has shown that;

2

1 263 1 1

12 2 1

417

KP

⎠

⎞

⎜

⎝

⎛

(12) where τ is surface tension [N/m]

The liquid phase consists of pure water, while the gas phase has multi components The transport of each species in the gas phase is governed by a general convection-diffusion equation in conjunction which the Stefan-Maxwell equations to account for multi species diffusion;

i g i g

N j

j j j

j j ij i g

m T

T D y

sat

P

P y x M

M y y M

M D y sat



=

⎥

⎥

⎥

⎥

⎦

⎤

⎢

⎢

⎢

⎢

⎣

⎡

∇ +

⋅

−

+

⎥

⎦

⎤

⎢

⎣

⎟

⎠

⎞

⎜

⎝

⎛∇ + ∇

−

−

⋅

=

ε ε

ρ

ε ρ

u

1

1

In order to account for geometric constraints of the porous media, the diffusivities are corrected using the Bruggemann correction formula [14];

5 1 ε

×

= ij

eff

ij D

The heat transfer in the gas diffusion layers is governed by the energy equation as follows;

( − sat g Cpg gT − keff g ∇ T ) = ( Tsolid − T ) − mphase∆ Hevap

⋅

where keff is effective electrode thermal conductivity [W/(m⋅K)]; the term [εβ(Tsolid−T)], on the right

hand side, accounts for the heat exchange to and from the solid matrix of the GDL The gas phase and the liquid phase are assumed to be in thermodynamic equilibrium, i.e., the liquid water and the gas phase are at the same temperature

The potential distribution in the gas diffusion layers is governed by;

⋅

∇ λe φ (16) where λe is electrode electronic conductivity [S/m]

In order to account for the magnitude of phase change inside the GDL, expressions are required to relate the level of over- and undersaturation as well as the amount of liquid water present to the amount of water undergoing phase change In the present work, the procedure of Berning and Djilali [18] was used

to account for the magnitude of phase change inside the GDL

2.2.3 Catalyst layers

The catalyst layer is treated as a thin interface, where sink and source terms for the reactants are implemented Due to the infinitesimal thickness, the source terms are actually implemented in the last grid cell of the porous medium At the cathode side, the sink term for oxygen is given by;

c O

F

M

S

4

2

where F is Faraday’s constant (96487 [C/mole]), i c is cathode local current density [A/m2], M is

molecular weight [kg/mole]

Whereas the sink term for hydrogen is specified as;

a H

F

M

S

2

2

where i a is anode local current density [A/m2]

The production of water is modelled as a source terms, and hence can be written as;

c O

H

O

F

M

S

2

2

The generation of heat in the cell is due to entropy changes as well as irreversibility's due to the activation overpotential [19];

i F

n

s

T

e

⎥

⎦

⎤

⎢

⎣

⎡

+

∆

−

= η

where q is heat generation [W/m2], ne is number of electrons transfer, s is specific entropy [J/(mole.K)],

ηact is activation overpotential (V)

The local current density distribution in the catalyst layers is modelled by the Butler-Volmer equation [18, 19];

⎥

⎦

⎤

⎢

⎣

⎡

⎟

⎠

⎞

⎜

⎝

⎛−

+

⎟

⎠

⎞

⎜

⎝

⎛

⎟

⎟

⎠

⎞

⎜

⎜

⎝

⎛

c act a ref

O

O

ref

c

c

RT

F RT

F C

C

i

2

⎥

⎦

⎤

⎢

⎣

⎡

⎟

⎠

⎞

⎜

⎝

⎛−

+

⎟

⎠

⎞

⎜

⎝

⎛

⎟

⎟

⎠

⎞

⎜

⎜

⎝

⎛

a act a ref

H

H

ref

a

a

RT

F RT

F C

C

i

2

2

where

2

H

C is local hydrogen concentration [mole/m3], ref

H

C

2 is reference hydrogen concentration [mole/m3],

2

O

C is local oxygen concentration [mole/m3], ref

O

C

2 is reference oxygen concentration [mole/m3], ref

a

i , is anode reference exchange current density, ref

c

i , is cathode reference exchange current density, R is universal gas constant (8.314 [J/(mole⋅K)]), αa is charge transfer coefficient, anode side, and αc is charge transfer coefficient, cathode side

2.2.4 Membrane

The balance between the electro-osmotic drag of water from anode to cathode and back diffusion from cathode to anode yields the net water flux through the membrane;

O

H

d

F

i M

n

where Nw is net water flux across the membrane [kg/(m2⋅s)], nd is electro-osmotic drag coefficient

The water diffusivity in the polymer can be calculated as follow [12];

⎥

⎦

⎤

⎢

⎣

⎡

⎟

⎠

⎞

⎜

⎝

×

T

303

1 2416 exp 10

3

.

The variable cW represents the number of water molecules per sulfonic acid group (i.e mol 2 equivalent 3−1

SO O

H ) The water content in the electrolyte phase is related to water vapour activity via [6, 7];

8 16 3 1

1 4 1 0 14 1 0 0 36 85

39 81 17

043

.

≥

=

≤

<

− +

=

≤

<

+

− +

=

a c

a a

c

a a

a a

c

W

W

W

(25)

The water vapour activity a given by;

sat

WP P

x

a = (26)

Heat transfer in the membrane is governed by;

⋅

where k mem is membrane thermal conductivity [W/(m⋅K)]

The potential loss in the membrane is due to resistance to proton transport across membrane, and is

governed by;

⋅

where λm is membrane ionic conductivity [S/m]

2.2.5 Potential drop across the cell

Useful work (electrical energy) is obtained from a fuel cell only when a current is drawn, but the actual

cell potential, (E cell ), is decreased from its equilibrium thermodynamic potential, (E), because of

irreversible losses The various irreversible loss mechanisms which are often called overpotentials, (η),

are defined as the deviation of the cell potential, (E cell), from the equilibrium thermodynamic potential

(E) The cell potential (E cell) is obtained by subtracting all overpotentials (η) (losses) from the

equilibrium thermodynamic potential (E) as the following expression;

Diff mem ohm act

cell E

The equilibrium potential is determined using the Nernst equation [16];

⎢⎣

× +

−

×

−

2

2 ln 2

1 ln

10 3085 4 15 298 10

83

0

229

.

O

P T T

2.2.5.1 Activation Overpotential

Activation overpotential (ηact) arises from the kinetics of charge transfer reaction across the

electrode-electrolyte interface In other words, a portion of the electrode potential is lost in driving the electron

transfer reaction Activation overpotential is directly related to the nature of the electrochemical reactions

and represents the magnitude of activation energy, when the reaction propagates at the rate demanded by

the current The activation overpotential can be divided into the anode and cathode overpotentials The

anode and cathode activation overpotentials are calculated from Butler-Volmer equation (21 and 22)

2.2.5.2 Ohmic Overpotential in Gas Diffusion Layers

The Ohmic overpotential (ηohm) is the potential loss due to current conduction through the anode and

cathode gas diffusion layers, and can be modeled by equation (16)

2.2.5.3 Membrane Overpotential

The membrane overpotential (ηmem) is related to the fact that an electric field is necessary in order to

maintain the motion of the hydrogen protons through the membrane This field is provided by the

existence of a potential gradient across the cell, which is directed in the opposite direction from the outer

field that gives us the cell potential, and thus has to be subtracted The overpotential in membrane is

calculated from the potential equation (28)

2.2.5.4 Diffusion Overpotential

Diffusion overpotential (ηDiff) is caused by mass transfer limitations on the availability of the reactants

near the electrodes The electrode reactions require a constant supply of reactants in order to sustain the

current flow When the diffusion limitations reduce the availability of a reactant, part of the available

reaction energy is used to drive the mass transfer, thus creating a corresponding loss in output voltage

Similar problems can develop if a reaction product accumulates near the electrode surface and obstructs

the diffusion paths or dilutes the reactants Mass transport loss becomes significant when the fuel cell is

operated at high current density This is created by the concentration gradient due to the consumption of

oxygen or fuel at the electrodes The mass transport loss at the anode is negligible compared to that at the cathode At the limiting current density, oxygen at the catalyst layer is depleted and no more current increase can be obtained from the fuel cell This is responsible for the sharp decline in potential at high current densities To reduce mass transport loss, the cathode is usually run at high pressure The anode and cathode diffusion overpotentials are calculated from the following equations [19];

⎟

⎟

⎠

⎞

⎜

⎜

⎝

⎛

−

=

c L

c c

Diff

i

i F

RT

,

2

⎟

⎟

⎠

⎞

⎜

⎜

⎝

⎛

−

=

a L

a a

Diff

i

i F

RT

,

2

GDL

O O

c

L

C

FD

i

δ

2 2

2

GDL

H H

a

L

C

FD

i

δ

2 2

2

where i L,c and i L,a are cathode and anode local limiting current density [A/m2], δGDL is the gas diffusion layer thickness [m], D is the diffusion coefficients [m2/s]

The diffusivity of oxygen and hydrogen are calculated from the following equations [19];

⎟

⎠

⎞

⎜

⎝

⎛

⎟

⎠

⎞

⎜

⎝

⎛

×

P

T

353 10

2

.

3

2 5

⎟

⎠

⎞

⎜

⎝

⎛

⎟

⎠

⎞

⎜

⎝

⎛

×

P

T

353 10

1

.

1

2 4

2.2.6 Cell power and efficiency

Once the cell potential is determined for a given current density, the output power density is found as;

cell

cell I E

where I is the cell operating (nominal) current density (A/m2)

The thermodynamic efficiency of the cell can be determined as [19];

2

2.

2

H H

cell

fc

LHV

M

F E

where LHV H2 is the lower heating value of hydrogen [J/kg]

2.3 Boundary conditions

Boundary conditions are specified at all external boundaries of the computational domain as well as boundaries for various mass and scalar equations inside the computational domain

2.3.1 Inlets

The inlet values at the anode and cathode are prescribed for the velocity, temperature and species concentrations (Dirichlet boundary conditions) The inlet velocity is a function of the desired current density, the geometrical area of the membrane, the channel cross-section area, and stoichiometric flow ratio The inlet velocities of air and fuel are calculated according to [20]:

ch c

c in

in O MEA c

c

in

A P

RT x

A F

I

4

, , ,

2 ζ

ch a

a in

in H MEA a

a

in

A P

RT x

A F

I

2

, , ,

2

ζ

where A MEA is the area of the MEA [m2], A ch is the cross sectional area of flow channel [m2], and ξ is the stoichiometric flow ratio

2.3.2 Outlets

At the outlets of the gas-flow channels, only the pressure is being prescribed as the desired electrode pressure; for all other variables, the gradient in the flow direction is assumed to be zero (Neumann boundary conditions)

2.3.3 External surfaces

At the external surfaces of the cell, temperature is specified and zero heat flux is applied at the surface of the conducting boundary surfaces

2.3.4 Interfaces inside the computational domain

Combinations of Dirichlet and Neumann boundary conditions are used to solve the electronic and protonic potential equations Dirichlet boundary conditions are applied at the land area (interface between the bipolar plates and the gas diffusion layers) Neumann boundary conditions are applied at the interface between the gas channels and the gas diffusion layers to give zero potential flux into the gas channels Similarly, the protonic potential field requires a set of potential boundary condition and zero flux boundary condition at the anode catalyst layer interface and cathode catalyst layer interface respectively

2.4 Computational procedure

2.4.1 Computational grid

The governing equations were discretized using a finite volume method and solved using a multi-physics general-purpose computational fluid dynamic (CFD) code The computational domains are divided into a finite number of control volumes (cells) All variables are stored at the centroid of each cell Interpolation

is used to express variable values at the control volume surface in terms of the control volume center values Stringent numerical tests were performed to ensure that the solutions were independent of the grid size A computational quadratic mesh consisting of a total of 11556 nodes and 59814 meshes was found to provide sufficient spatial resolution (Figure 2) The coupled set of equations was solved iteratively, and the solution was considered to be convergent when the relative error was less than 1.0×10-6 in each field between two consecutive iterations The geometric and the base case operating conditions are listed in Table 1 Values of the electrochemical transport parameters for the base case operating conditions are taken from reference [20] and are listed in Table 2

2.4.2 Solution algorithm

The solution begins by specifying a desired current density of the cell to be used for calculating the inlet flow rates at the anode and cathode sides An initial guess of the activation overpotential is obtained from the desired current density using the Butler-Volmer equation Then follows by computing the flow fields for velocities u,v,w, and pressure P Once the flow field is obtained, the mass fraction equations are solved for the mass fractions of oxygen, hydrogen, water vapor, and nitrogen Scalar equations are solved last in the sequence of the transport equations for the temperature field in the cell and potential fields in the gas diffusion layers and the membrane The local current densities are solved based on the Butler-Volmer equation After the local current densities are obtained, the local activation overpotentials can be readily calculated from the Butler-Volmer equation The local activation overpotentials are updated after each global iterative loop Convergence criteria are then performed on each variable and the procedure is repeated until convergence The properties and then source terms are updated after each global iterative loop based on the new local gas composition and temperature The strength of the current model is clearly to perform parametric studies and explore the impact of various parameters on the transport mechanisms and on fuel cell performance The new feature of the algorithm developed in this work is its capability for accurate calculation of the local activation overpotentials, which in turn results in improved prediction of the local current density distribution The flow diagram of the algorithm is shown in Figure

3

Figure 2 Computational mesh for micro PEM fuel cell with nature inspired gas flow channels

Table 1 Geometrical and operational parameters for base case conditions

Wet membrane thickness (Nafion® 117) δmem 50 µ m

Hydrogen reference mole fraction ref

H

x

2

0.84639

O

x

2

0.17774

Relative humidity of inlet fuel and air ψ 100 %